Abstract
In this paper we present some novel fixed point theorems for a family of contractions depending on two functions (that are not defined on t = 0 ) and on some parameters that we have called multiparametric contractions. We develop our study in the setting of b-metric spaces because they allow to consider some families of functions endowed with b-metrics deriving from similarity measures that are more general than norms. Taking into account that the contractivity condition we will employ is very general (of Hardy-Rogers type), we will discuss the validation and usage of this novel condition. After that, we introduce the main results of this paper and, finally, we deduce some consequences of them which illustrates the wide applicability of the main results.
Highlights
The field of Fixed Point Theory has very recently undergone a great development, mainly due to the great number of contractivity conditions, especially in two directions: by considering new terms and by involving auxiliary functions
We present some novel fixed point theorems for a family of contractions depending on two functions and on some parameters that we have called multiparametric contractions
We develop our study in the setting of b-metric spaces because they are, in our opinion, a very successful context because they allow to consider some important families of functions endowed with b-metrics deriving from similarity measures that are more general than norms
Summary
The field of Fixed Point Theory has very recently undergone a great development, mainly due to the great number of contractivity conditions, especially in two directions: by considering new terms and by involving auxiliary functions. D ( x, y) for all x, y ∈ X such that x 6= y Such kind of contractivity conditions can only be verified by pairs of distinct points of the metric space (see [12]). This new family of hypotheses allowed the researcher to realize that, in many cases, contractivity conditions became trivial when the pair of points are equal, that is, x = y. A lot of results were introduced by assuming that the contractivity condition must be only verified for distinct points. We introduce the main results of this paper and, we deduce some consequences of them which illustrates the wide applicability of the main results
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